JEE Main 2023 · 12 April · morning · Single correct · +4 / −1
Three forces F₁=10 N, F₂=8 N, F₃=6 N are acting on a particle of mass 5 kg. The forces F₂ and F₃ are applied perpendicularly so that particle remains at rest. If the force F₁ is removed, then the acceleration of the particle is:
- (a) 4.8 ms⁻²
- (b) 7 ms⁻²
- (c) 2 ms⁻²
- (d) 0.5 ms⁻²
Answer and solution
Answer (c) 2 ms⁻²
Solution
Physics sir · 4 steps
At rest means F₂ and F₃ cancel F₁, so removing F₁ leaves their 10 N resultant.
- Equilibrium first. The particle is at rest, so the three forces add to zero. That means the resultant of F₂ and F₃ is equal in size and opposite in direction to F₁.
- Add F2 and F3. F₂ and F₃ are perpendicular, so add them with Pythagoras: √(8² + 6²) = √100 = 10 N. This matches F₁ = 10 N, as it must.
- Remove F1. Once F₁ is gone, nothing balances F₂ and F₃. The net force on the particle is their resultant, 10 N, pointing opposite to where F₁ was.
a = Fₙₑₜ/m = (10 N)/(5 kg) = 2 m s⁻²
- So. The acceleration is 2 m s⁻², option (c).
The idea to keep. If a body is in equilibrium and you remove one force, the net force left is equal and opposite to the removed force. You do not even need the other forces' directions.
Answer from the NTA final answer key. Solution by PrepWiser.